The compressive plastic strength of nanosized single crystal metallic pillars is known to depend on the diameter D, but little attention has been given to the pillar height h. The important role of h is analyzed here, observing the suppression of generalized crystal plasticity below a critical value hCR that can be estimated a priori. Novel in-situ compression tests on regular pillars (D = 300-900 nm) as well as nanobuttons (i.e. very short pillars with h less than hCR, such as D = 200 nm and h < 120 nm in this case) show that the latter ones are exceedingly harder than ordinary Ni pillars, withstanding stresses greater than 2 GPa. This h-controlled transition in the plastic behaviour is accompanied by extrinsic plastic effects in the harder nanobuttons. Such effects normally arise as Saint-Venant's assumption ceases to be accurate. Some bias related to those effects is identified and removed from test data. Our results underline that nanoscale testing is challenging when current methodology and technology are pushed to the limit.